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C₂×#22311 #6376680

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4)(5,8)(6,10)(7,9)(11,12)(13,15)(14,17)(16,18)(19,20,24,21,23,26,22,25);(3,5,7,6)(4,8,9,10)(11,13,15,12)(14,17,18,16)(19,21,24,26,23,25,22,20);(3,6,7,5)(4,8,9,10)(12,13)(16,17)(19,22,23,24)(20,25,26,21);(11,14,15,18)(12,16,13,17)(19,22,23,24)(20,25,26,21)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6283876);